Question

Find the point on the line 4x+3y-4=0 which is closest to the point (5,2)

Answer 1

A line from (5,2) perpendicular to the curve will have the shortest distance to the curve.

The slope of the graph is -4/3, so the normal has slope 3/4

So, now you have a point and a slope, so the perpendicular line through (5,2) is

y-2 = 3/4 (x-5)
y = 3/4 x - 7/4

These two lines intersect at (37/25,-16/25)

Answer 2

Thank you for your help!